Open Access
2014 Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps
Ying Du, Changlin Mei
Abstr. Appl. Anal. 2014: 1-11 (2014). DOI: 10.1155/2014/159107


To realize the applications of stochastic differential equations with jumps, much attention has recently been paid to the construction of efficient numerical solutions of the equations. Considering the fact that the use of the explicit methods often results in instability and inaccurate approximations in solving stochastic differential equations, we propose two implicit methods, the θ-Taylor method and the balanced θ-Taylor method, for numerically solving the stochastic differential equation with jumps and prove that the numerical solutions are convergent with strong order 1.0. For a linear scalar test equation, the mean-square stability regions of the methods are derived. Finally, numerical examples are given to evaluate the performance of the methods.


Download Citation

Ying Du. Changlin Mei. "Implicit Numerical Solutions for Solving Stochastic Differential Equations with Jumps." Abstr. Appl. Anal. 2014 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07021834
MathSciNet: MR3246315
Digital Object Identifier: 10.1155/2014/159107

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
Back to Top